Converse of the Angle Bisector Conjecture

Geometry doesn't come easily for Grace. It's a given that she's brilliant, she's in the Gifted and Talented Program in our Home School, but it can be downright challenging for this child of mine to grasp different tools and use them for solving problems. She can hardly handle a pencil, let alone a compass, a straight-edge, "why can't we just call it a ruler?!?!?!?!" and a protractor.

Today her challenge came with the following question from her textbook:

"In this lesson you discovered the Angle Bisector Conjecture. Write the converse of the Angle Bisector Conjecture. Do you think it's true? Why or why not?"

The first challenge came when she tried to remember what this conjecture stated. Of course, she was supposed to have this term neatly penned in her Geometry notebook and firmly embedded in her brain. Instead, she thumbed through the book until she found the definition and mumbled it back to me. Urging her to try to grasp the concept, I made her repeat the definition.

"Pretend you're the teacher. You learn it, then you teach it to me," I brilliantly challenged. This time she clearly was able to illustrate and explain this geometric concept.

"OK," I said brightly. "Now, what is the converse of this conjecture?

Blank stares accompanied by giggles and fidgets clearly shouted volumes to me.

Backing up my track, I asked, "Grace, what is converse?"

Meekly, she speculated, "A type of shoes?"

"What?" I was flabbergasted. (Doesn't that sound like the right adjective to put here?)

"A cool type of shoes?....they're really, really cool shoes."

I'm either going to have to buy her a dictionary, Geometry for Dummies or a new pair of tennis shoes, preferably Converse.